Abstract

Let G H be a reductive symmetric space and suppose V is an admissible ( g , K )-module of finite length possessing a linear functional T ϵ Vsu which is fixed by h and H ∩ K . We prove that V can be mapped equivariantly into C ∞ ( G H ) such that T becomes the pull-back of the Dirac measure at the origin. Essential in the proof is the fact that the formal power series of certain matrix coefficients of V satisfy a system of differential equations with regular singularities.

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